Electrical conductivity and permittivity has been the subject of intensive study in the physical and biological sciences. Extensive experimental studies and theoretical discoveries in physics and materials science have surrounded the microscopic origins of electrical conductivity and permittivity. Biological tissue has long been recognized as an electrically active medium. Given the critical importance of electrical signal transduction in physiology, interest in bioelectrical properties has been ongoing. Thus, knowledge of the internal distribution of these electrical properties in intact materials and organisms can advance fundamental understandings, promote new discoveries, and facilitate novel diagnostics and interventions in a diverse array of fields.
Despite all of this active interest, attempts to map the spatial distribution of electrical properties, in vivo, in intact human organs, or even heterogeneous materials have met with limited success. Attempts to map electrical properties noninvasively have struggled with underlying instability and ill-posedness. Typically, either invasive probes have been used, which can disturb the local environment and preclude true cross-sectional mapping, or alternatively, “electrical prospection” approaches such as Electrical Impedance Tomography (“EIT”) have been devised in which surface-based measurements can be converted to property maps via notoriously ill-posed inverse problems. EIT, and similar techniques, have been deployed for diagnosis or surveillance of disease, but fundamental limitations in resolution and robustness have thus far impeded widespread use.
Accurate volumetric maps of electrical properties in situ can be of interest not only for basic biophysical understanding of tissue and material structure, but also for a wide array of applications in human health. Tumors, for example, can be known to have markedly different electrical properties from normal tissue. Brain, heart, and muscle are all electrical organs, with the ability to carry current and store charge being fundamental to their operation, and with derangements in these functions being associated with disease processes ranging from epilepsy to arrhythmia to myopathy. Various interventions, such as transcranial magnetic stimulation (“TMS”) or radiofrequency (“RF”) ablation, can benefit from individualized maps of electrical properties, as would diagnostic techniques such as electro- or magneto-encephalography (“EEG” or “MEG”), which can be founded upon electromagnetic source localization.
Magnetic Resonance Imaging (“MRI”) can provide noninvasive volumetric information about the interior magnetic environment of tissue or materials, and various attempts have been made to use this information to circumvent the ill-posed inverse problem of electrical prospection. In particular, MRI can be used to map the distribution of internal magnetic fields resulting from currents or fields applied to a body. This information can be used to deduce distributions of electrical properties in vivo. However, certain key information can be missing from magnetic resonance (“MR”)-based measurements. For example, the absolute phase distribution of the RF magnetic field can generally be considered to be fundamentally inaccessible due to the nature of signal excitation and detection in magnetic resonance. The absolute distribution of RF signal sensitivity can be fundamentally entangled with the unknown distribution of magnetization in a body. It has been recognized that access to this absolute field-related information can facilitate calculation of useful quantities such as local energy deposition in MRI, in addition to the electrical property distribution. Recently, various ingenious approximations have been applied to derive or bypass absolute RF phase, generally involving symmetry assumptions about the body or the probe used to image it. These approximations, however, can break down precisely when fields can be most perturbed by tissue properties, (e.g., at high operating frequencies) when MR-based techniques should otherwise perform best, and when local energy deposition can be of most concern.
Thus, there may be a need for providing exemplary systems, methods and computer-accessible mediums for facilitating noninvasive mapping of electrical properties of tissue or materials, which addresses both the prior problems of noninvasive electrical property mapping, and the more recent and circumscribed problem of determination of absolute RF phase and magnetization distribution in MRI, and which can overcome at least some of the deficiencies described herein above.